arXiv research

CROC identifies the earliest-changing stream as the root cause in multi-stream data.

New definition of patient-specific root causes of disease using counterfactuals.

Let $C$ be a curve in a closed orientable surface $F$ of genus $g \geq 2$ that separates $F$ into subsurfaces $\widetilde {F_i}$ of genera $g_i$, for $i = 1,2$. We study the set of roots in $\Mod(F)$ of the Dehn twist $t_C$ about $C$. All roots arise from pairs of $C_{n_i}$-actions on the $\widetilde{F_i}$, where $n=\l…

Margalit and Schleimer constructed nontrivial roots of the Dehn twist about a nonseparating curve. We prove that the conjugacy classes of roots of the Dehn twist about a nonseparating curve correspond to the conjugacy classes of periodic maps with certain conditions. Futhermore, we give data set which determine the con…

New method estimates root-directed tree from extreme data.

New proof for symmetric spaces with rectangular lattices.

The paper proposes a new probability distribution for rooted trees.

Guarantees uniform convergence for square-root Lipschitz losses.

The study of random positive 3-strand braids reveals patterns in the roots of their Alexander polynomials.

Study finds price impact follows a 'double' square-root law, suggesting mechanical origin.

Study infers tree topology from customer data using contrastive learning.

A \textit{multicurve} $\C$ on a closed orientable surface is defined to be a finite collection of disjoint non-isotopic essential simple closed curves. The Dehn twist $t_{\C}$ about $\C$ is the product of the Dehn twists about the individual curves. In this paper, we give necessary and sufficient conditions for the exi…

Many independent studies on stocks and futures contracts have established that market impact is proportional to the square-root of the executed volume. Is market impact quantitatively similar for option markets as well? In order to answer this question, we have analyzed the impact of a large proprietary data set of opt…

The notion of market impact is subtle and sometimes misinterpreted. Here we argue that impact should not be misconstrued as volatility. In particular, the so-called ``square-root impact law'', which states that impact grows as the square-root of traded volume, has nothing to do with price diffusion, i.e. that typical p…

Performance monitoring, anomaly detection, and root-cause analysis in complex cyber-physical systems (CPSs) are often highly intractable due to widely diverse operational modes, disparate data types, and complex fault propagation mechanisms. This paper presents a new data-driven framework for root-cause analysis, based…

A new probability distribution on full rooted trees helps in model selection.

Two-root Riemannian manifolds have no odd-dimensional examples.

In this paper, we characterize locally dually flat generalized m-th root Finsler metrics. Then we find a condition under which a generalized m-th root metric is projectively related to a m-th root metric. Finally, we prove that if a generalized m-th root metric is conformal to a m-th root metric, then both of them redu…

The study confirms that market volatility can be explained by correlated metaorders impacting prices in a square-root fashion.

Algorithm generates realistic metaorders from public trade data.

Novel approach integrates Multivariate Square-root Lasso into Synthetic Control for high-dimensional data.

TPSQRs model longitudinal event data, detecting ADRs from EHRs.

Uniqueness of quasi-roots explored in right-angled Artin groups.

Study differential properties of matrix square roots in specific cases.

Identifies root causes of outliers in unknown cyclic graphs.

D. Margalit and S. Schleimer found examples of roots of the Dehn twist about a nonseparating curve in a closed orientable surface, that is, homeomorphisms whose nth power is isotopic to the Dehn twist. Our main theorem gives elementary number-theoretic conditions that describe the values of n for which an nth root exis…

Root Laplacian Eigenmaps help in spectral embedding of graphs.

Margalit and Schleimer observed that Dehn twists on orientable surfaces have nontrivial roots. We investigate the problem of roots of a Dehn twist t_c about a nonseparating circle c in the mapping class group M(N_g) of a nonorientable surface N_g of genus g. We explore the existence of roots and, following the work of …

New model identifies patient-specific disease root causes.

We apply an asymmetric version of Kirman's herding model to volatile financial markets. In the relation between returns and agent concentration we use the square root law proposed by Zhang. This can be derived by extending the idea of a critical mean field theory suggested by Plerou et al. We show that this model is eq…

A new method simulates square-root processes efficiently.

Enhanced ROOT-SGD optimizes stochastic optimization with diminishing stepsizes.

Paper adapts causal analysis for time-dependent systems, especially energy management.

In this paper, we prove that every m-th root metric with isotropic mean Berwald curvature reduces to a weakly Berwald metric. Then we show that an m-th root metric with isotropic mean Landsberg curvature is a weakly Landsberg metric. We find necessary and sufficient condition under which conformal $β$-change of an m-th…

Automorphisms of Lie algebras and their root systems are fully lifted.

Root's barrier is continuous and finite under certain conditions.

In this paper, we find a condition under which a Finsler space with Kropina change of mth-root metric is projectively related to a mth-root metric and also we find a condition under which this Kropina transformed mth-root metric is locally dually flat. Moreover we find the condition for its Projective flatness.

Optimizes quantile and semi-adversarial regret with novel root-logarithmic regularizers.

Identifies patient-specific root causes of disease using structural equation models.

In this paper, we consider Kropina change of $m$-th root Finsler metrics. We find necessary and sufficient condition under which the Kropina change of an $m$-th root Finsler metric be locally dually flat. Then we prove that the Kropina change of an $m$-th root Finsler metric is locally projectively flat if and only if …

The square root velocity framework is a method in shape analysis to define a distance between curves and functional data. Identifying two curves if they differ by a reparametrisation leads to the quotient space of unparametrised curves. In this paper we study analytical and topological aspects of this construction for …

A fundamental challenge in semi-supervised learning lies in the observed data's disproportional size when compared with the size of the data collected with missing outcomes. An implicit understanding is that the dataset with missing outcomes, being significantly larger, ought to improve estimation and inference. Howeve…

Defines a generalized string concept for abstract root systems.

Unlike traditional programs (such as operating systems or word processors) which have large amounts of code, machine learning tasks use programs with relatively small amounts of code (written in machine learning libraries), but voluminous amounts of data. Just like developers of traditional programs debug errors in the…

Continuity of roots of hyperbolic polynomials with smooth coefficients.

Transforms curves and surfaces for efficient geometric analysis.

Polynomials' roots count tied to surface umbilics.

In this paper, we characterize locally dually flat and Antonelli $m$-th root Finsler metrics. Then, we show that every $m$-th root Finsler metric of isotropic mean Berwald curvature reduces to a weakly Berwald metric.